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Search: id:A123588
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| A123588 |
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Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial 1 - T(n, x^(1/2))^2, where T(n,x) is the n-th Chebyshev polynomial of the first kind, evaluated at x (0<=k<=n). |
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+0
6
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| 0, 1, -1, 0, 4, -4, 1, -9, 24, -16, 0, 16, -80, 128, -64, 1, -25, 200, -560, 640, -256, 0, 36, -420, 1792, -3456, 3072, -1024, 1, -49, 784, -4704, 13440, -19712, 14336, -4096, 0, 64, -1344, 10752, -42240, 90112, -106496, 65536, -16384, 1, -81, 2160, -22176, 114048, -329472, 559104, -552960, 294912
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.
G. B. Shabat and I. A. Voevodskii, Drawing curves over number fields, The Grothendieck Festschift, vol. 3, Birkhaeuser, 1990, pp. 199-227.
G. B. Shabat and A. Zvonkin, Plane trees and algebraic numbers, Contemporary Math., 1994, vol. 178, pp. 233-275.
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LINKS
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Yuri Matiyasevich, Generalized Chebyshev polynomials.
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EXAMPLE
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Polynomials:
0,
1 - x^2,
4 x^2 - 4 x^4,
1 - 9 x^2 + 24 x^4 - 16 x^6,
16 x^2 - 80 x^4 + 128 x^6 - 64 x^8,
1 - 25 x^2 + 200 x^4 - 560 x^6 + 640 x^8 - 256 x^10
Triangle starts:
0;
1,-1;
0,4,-4;
1,-9,24,-16;
0,16,-80,128,-64;
1,-25,200,-560,640,-256;
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MAPLE
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with(orthopoly): for n from 0 to 9 do seq(coeff(expand((1-T(n, sqrt(x))^2)), x, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Sequence in context: A016706 A138679 A080721 this_sequence A106026 A096078 A140313
Adjacent sequences: A123585 A123586 A123587 this_sequence A123589 A123590 A123591
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KEYWORD
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sign,tabl
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Nov 12 2006
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EXTENSIONS
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Edited by njas, Dec 03 2006
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